Looking at things like NATO vs the Warsaw Pact, or the US vs China/the Soviets/the Japanese, there seems to be a trend to favor "blue" for Western forces and red for the Eastern forces.
This trend is continued in video games where blue represents some arbitrary "good guys" and red is the enemy.
How did this come about? Do other cultures use a similar coloring scheme, or do Mongolians think of Americans as purple and the Japanese as orange, for example?
At the US Army Command and General Staff College, promising young West Point graduates, who are working on the equivalent of a Masters Degree, are given many problems to work through. Traditionally, the smaller but better equipped side was the Blue force. The larger, but less mobile and less well equipped side was the Red force.
This school can trace its roots back to 1881, when William Tecumseh Sherman was installed as the first director of the US Army School of Application for Infantry and Cavalry. This was after the US Army had stopped looking at the French Army as being the masters of war, and instead began to look at the much more recent and copious data they compiled from their own Civil War experiences. After World War II, the US Army began to train the armies of other friendly nations and that is how the concept of a Blue team and Red team spread to other parts of the world.
Source: "A Country Made by War: The Military History of the United States" by Geoffrey Perret.
For that matter -- why are red and blue the most common flag colors in general?
During the Russian Revolution, the Communists took a red star, and later, a red flag, as their symbol. Those opposing them took white as their symbol. Because of this, red came to be associated with communism and other communist states adopted red for their flag, etc. in the US, calling someone "a red" was tantamount to saying they were a communist. When the communists took over China, it was referred to as "Red China" to distinguish it from Taiwan, which was not communist.
Japan sometimes gets associated with red too, not because of communism but because it is "The Land of the Rising Sun" and so it's flag has a big red sun on it.
That's why you often see red associates with those countries, even though now, Russia is no longer communist and has a white, blue, and red flag.
But there are other factors at play. For example, mapmakers took pink to be the color for all areas of the British Empire in the 19th-20th centuries, so they are usually pink even today, not blue.